A218476 Number of 3n-length 6-ary words, either empty or beginning with the first letter of the alphabet, that can be built by repeatedly inserting triples of identical letters into the initially empty word.

1, 1, 16, 331, 7746, 195011, 5153626, 140995716, 3958980906, 113434797571, 3303283462836, 97478710394451, 2908594804576416, 87605427983818356, 2659959016770389896, 81330226479826092536, 2501989790308939894026, 77386492111973937031491, 2405093253522796180052056

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

a(n) = 1/n * Sum_{j=0..n-1} C(3*n,j)*(n-j)*5^j for n>0, a(0) = 1.

Recurrence: 2*n*(2*n-1)*(9*n-11)*a(n) = 3*(2997*n^3 - 5769*n^2 + 2754*n - 200)*a(n-1) - 3240*(3*n-5)*(3*n-4)*(9*n-2)*a(n-2). - Vaclav Kotesovec, Aug 31 2014

a(n) ~ 3^(3*n-7/2) * 5^(n+1) / (sqrt(Pi) * n^(3/2) * 4^n). - Vaclav Kotesovec, Aug 31 2014

Maple

a:= n-> `if`(n=0, 1, add(binomial(3*n, j)*(n-j)*5^j, j=0..n-1)/n):
seq(a(n), n=0..20);

Crossrefs

Column k=6 of A213027.

Sequence in context: A246876 A176128 A223394 * A240344 A068368 A013993

Adjacent sequences: A218473 A218474 A218475 * A218477 A218478 A218479

Keyword

nonn

Author

Alois P. Heinz, Oct 29 2012

Status

approved